Subgroups — C₇×#62846 #13240062

Order 1792.

7390 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#3521	C₂	1	8	yes	maximal, complemented
2	C₇×#3519	C₂	1	8	yes	maximal, complemented
3	C₇×#3514	C₂	1	8	yes	maximal, complemented
4	C₇×#3513	C₂	1	8	yes	maximal, complemented
5	C₇×#3506	C₂	1	2	yes	maximal, complemented
6	C₇×#3505	C₂	1	4	yes	maximal, complemented
7	C₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
8	C₇×#3496	C₂	1	1	yes	maximal, characteristic, complemented
9	C₇×#3493	C₂	1	2	yes	maximal, complemented
10	C₇×#3490	C₂	1	4	yes	maximal, complemented
11	C₇×#3484	C₂	1	2	yes	maximal, complemented
12	C₇×#3460	C₂	1	2	yes	maximal, complemented
13	C₇×#3459	C₂	1	4	yes	maximal, complemented
14	C₇×#3455	C₂	1	2	yes	maximal, complemented
15	C₂×C₇×#538	C₂	1	4	yes	maximal, complemented
16	C₄×C₇×H(5,𝔽₂)	C₂	1	2	yes	maximal, complemented
17	C₂×C₇×#518	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×C₇×H(5,𝔽₂)	C₂²	1	2	yes	—
19	C₂³×C₇×D₄	C₂²	1	1	yes	characteristic
20	C₇×#559	C₂²	1	8	yes	complemented
21	C₇×#556	C₂²	1	8	yes	complemented
22	C₇×#556	C₂²	1	4	yes	complemented
23	C₇×#555	C₂²	1	8	yes	complemented
24	C₇×#555	C₂²	1	4	yes	complemented
25	C₇×#554	C₂²	1	4	yes	complemented
26	C₇×#554	C₂²	1	8	yes	complemented
27	C₇×#553	C₂²	1	8	yes	complemented
28	C₇×#553	C₂²	1	8	yes	complemented
29	C₇×#553	C₂²	1	16	yes	complemented
30	C₇×#553	C₂²	1	8	yes	complemented
31	C₇×#552	C₂²	1	8	yes	complemented
32	C₇×#552	C₂²	1	8	yes	complemented
33	C₇×#551	C₂²	1	16	yes	complemented
34	C₇×#551	C₂²	1	16	yes	complemented
35	C₇×#551	C₂²	1	16	yes	complemented
36	C₇×#550	C₂²	1	4	yes	complemented
37	C₇×D₄×Q₈	C₂²	1	4	yes	complemented
38	C₇×#548	C₂²	1	8	yes	complemented
39	C₇×#547	C₂²	1	4	yes	complemented
40	C₇×#547	C₂²	1	4	yes	complemented
41	C₇×#546	C₂²	1	8	yes	complemented
42	C₇×#546	C₂²	1	8	yes	complemented
43	C₇×#546	C₂²	1	16	yes	complemented
44	C₇×#546	C₂²	1	16	yes	complemented
45	C₇×#546	C₂²	1	8	yes	complemented
46	C₇×#546	C₂²	1	8	yes	complemented
47	C₇×D₄²	C₂²	1	8	yes	complemented
48	C₇×D₄²	C₂²	1	8	yes	complemented
49	C₇×D₄²	C₂²	1	4	yes	complemented
50	C₇×#544	C₂²	1	2	yes	complemented
51	C₇×#543	C₂²	1	4	yes	complemented
52	C₇×#542	C₂²	1	4	yes	complemented
53	C₇×#542	C₂²	1	4	yes	complemented
54	C₇×#542	C₂²	1	8	yes	complemented
55	C₇×#541	C₂²	1	4	yes	complemented
56	C₇×#540	C₂²	1	4	yes	complemented
57	C₇×#540	C₂²	1	8	yes	complemented
58	C₇×#539	C₂²	1	4	yes	complemented
59	C₇×#539	C₂²	1	4	yes	complemented
60	C₇×#539	C₂²	1	16	yes	complemented
61	C₇×#538	C₂²	1	4	yes	complemented
62	C₇×#538	C₂²	1	8	yes	complemented
63	C₇×#538	C₂²	1	4	yes	complemented
64	C₇×#538	C₂²	1	8	yes	complemented
65	C₇×#538	C₂²	1	8	yes	complemented
66	C₇×#538	C₂²	1	16	yes	complemented
67	C₇×#538	C₂²	1	16	yes	complemented
68	C₇×#538	C₂²	1	16	yes	complemented
69	C₇×#537	C₂²	1	2	yes	complemented
70	C₇×#535	C₂²	1	4	yes	complemented
71	C₇×#534	C₂²	1	8	yes	complemented
72	C₇×#534	C₂²	1	4	yes	complemented
73	C₇×#533	C₂²	1	2	yes	complemented
74	C₇×#532	C₂²	1	2	yes	complemented
75	C₇×#532	C₂²	1	8	yes	complemented
76	C₇×#529	C₂²	1	8	yes	complemented
77	C₇×#529	C₂²	1	8	yes	complemented
78	C₇×#529	C₂²	1	8	yes	complemented
79	C₇×#529	C₂²	1	16	yes	complemented
80	C₇×#529	C₂²	1	8	yes	complemented
81	C₂×C₇×#126	C₂²	1	8	yes	complemented
82	C₂×C₇×#124	C₂²	1	8	yes	complemented
83	C₇×#525	C₂²	1	4	yes	complemented
84	C₇×#525	C₂²	1	8	yes	complemented
85	C₇×#525	C₂²	1	8	yes	complemented
86	C₇×#525	C₂²	1	16	yes	complemented
87	C₂×C₇×#123	C₂²	1	8	yes	complemented
88	C₂×C₇×C₂²⋊Q₈	C₂²	1	4	yes	complemented
89	C₂×C₇×#121	C₂²	1	8	yes	complemented
90	C₂×C₇×#121	C₂²	1	4	yes	complemented
91	C₂×C₇×#120	C₂²	1	8	yes	complemented
92	C₇×#520	C₂²	1	4	yes	complemented
93	C₇×#520	C₂²	1	8	yes	complemented
94	C₇×#518	C₂²	1	2	yes	—
95	C₇×#518	C₂²	1	8	yes	complemented
96	C₇×#518	C₂²	1	8	yes	complemented
97	C₇×#518	C₂²	1	8	yes	complemented
98	C₇×#518	C₂²	1	8	yes	complemented
99	C₄×C₇×#41	C₂²	1	4	yes	complemented
100	C₄×C₇×#41	C₂²	1	8	yes	complemented
101	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
102	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic
103	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
104	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₄×C₇×D₄	C₂²	1	2	yes	complemented
106	C₂×C₄×C₇×D₄	C₂²	1	1	yes	characteristic, complemented
107	C₂×C₄×C₇×D₄	C₂²	1	8	yes	complemented
108	C₂×C₄×C₇×D₄	C₂²	1	8	yes	complemented
109	C₂×C₇×#117	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₇×#117	C₂²	1	1	yes	characteristic, complemented
111	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
112	C₂²×C₇×C₂²⋊C₄	C₂²	1	2	yes	complemented
113	#62846	C₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
114	C₂⁵×C₇	C₂³	1	2	yes	—
115	C₇×H(5,𝔽₂)	—	2	16	no	—
116	C₂×C₇×#41	C₂³	1	4	yes	—
117	C₂×C₇×#41	C₂³	1	8	yes	—
118	C₂×C₇×#41	C₂³	1	8	yes	complemented
119	C₂×C₇×#41	C₂³	1	8	yes	complemented
120	C₂²×C₇×Q₈	C₂³	1	4	yes	complemented
121	C₂²×C₇×D₄	—	2	8	no	—
122	C₂²×C₇×D₄	C₂³	1	2	yes	—
123	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
124	C₂²×C₇×D₄	C₂³	1	8	yes	—
125	C₂²×C₇×D₄	C₂³	1	8	yes	—
126	C₂²×C₇×D₄	C₂³	1	8	yes	—
127	C₂²×C₇×D₄	C₂³	1	8	yes	—
128	C₂²×C₇×D₄	C₂³	1	8	yes	—
129	C₂²×C₇×D₄	C₂³	1	1	yes	characteristic
130	C₂²×C₇×D₄	C₂³	1	4	yes	complemented
131	C₂³×C₄×C₇	C₂³	1	1	yes	characteristic
132	C₂³×C₄×C₇	C₂³	1	2	yes	—
133	C₂³×C₄×C₇	C₂³	1	2	yes	—
134	C₂³×C₄×C₇	C₂³	1	2	yes	—
135	C₂³×C₄×C₇	C₂³	1	2	yes	—
136	C₂³×C₄×C₇	C₂³	1	8	yes	complemented
137	C₇×C₄⋊Q₈	C₂³	1	2	yes	complemented
138	C₇×C₄⋊Q₈	C₂³	1	8	yes	complemented
139	C₇×C₄⋊Q₈	C₂³	1	2	yes	complemented
140	C₇×C₄⋊Q₈	C₂³	1	2	yes	complemented
141	C₇×#127	C₂³	1	8	yes	—
142	C₇×#127	C₂³	1	2	yes	complemented
143	C₇×#126	C₂³	1	8	yes	—
144	C₇×#126	C₂³	1	16	yes	—
145	C₇×#126	C₂³	1	8	yes	—
146	C₇×#126	C₂³	1	16	yes	complemented
147	C₇×#126	C₂³	1	16	yes	complemented
148	C₇×#126	C₂³	1	8	yes	complemented
149	C₇×#126	C₂³	1	16	yes	complemented
150	C₇×#126	C₂³	1	8	yes	complemented
151	C₇×#125	C₂³	1	8	yes	complemented
152	C₇×#125	C₂³	1	8	yes	complemented
153	C₇×#125	C₂³	1	8	yes	complemented
154	C₇×#125	C₂³	1	8	yes	complemented
155	C₇×#125	C₂³	1	4	yes	complemented
156	C₇×#124	C₂³	1	8	yes	—
157	C₇×#124	C₂³	1	16	yes	—
158	C₇×#124	C₂³	1	8	yes	—
159	C₇×#124	C₂³	1	8	yes	—
160	C₇×#124	C₂³	1	16	yes	complemented
161	C₇×#124	C₂³	1	16	yes	complemented
162	C₇×#124	C₂³	1	8	yes	complemented
163	C₇×#124	C₂³	1	4	yes	complemented
164	C₇×#123	C₂³	1	8	yes	—
165	C₇×#123	C₂³	1	16	yes	—
166	C₇×#123	C₂³	1	8	yes	—
167	C₇×#123	C₂³	1	16	yes	—
168	C₇×#123	C₂³	1	8	yes	—
169	C₇×#123	C₂³	1	16	yes	complemented
170	C₇×#123	C₂³	1	16	yes	complemented
171	C₇×#123	C₂³	1	8	yes	complemented
172	C₇×#123	C₂³	1	16	yes	complemented
173	C₇×#123	C₂³	1	16	yes	complemented
174	C₇×#123	C₂³	1	16	yes	complemented
175	C₇×#123	C₂³	1	8	yes	complemented
176	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
177	C₇×C₂²⋊Q₈	C₂³	1	8	yes	—
178	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
179	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
180	C₇×C₂²⋊Q₈	C₂³	1	4	yes	—
181	C₇×C₂²⋊Q₈	C₂³	1	8	yes	complemented
182	C₇×C₂²⋊Q₈	C₂³	1	8	yes	complemented
183	C₇×C₂²⋊Q₈	C₂³	1	8	yes	complemented
184	C₇×C₂²⋊Q₈	C₂³	1	8	yes	complemented
185	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
186	C₇×C₂²⋊Q₈	C₂³	1	8	yes	complemented
187	C₇×C₂²⋊Q₈	C₂³	1	8	yes	complemented
188	C₇×C₂²⋊Q₈	C₂³	1	16	yes	complemented
189	C₇×C₂²⋊Q₈	C₂³	1	8	yes	complemented
190	C₇×#121	C₂³	1	8	yes	—
191	C₇×#121	C₂³	1	4	yes	—
192	C₇×#121	C₂³	1	8	yes	—
193	C₇×#121	C₂³	1	16	yes	—
194	C₇×#121	C₂³	1	4	yes	—
195	C₇×#121	C₂³	1	16	yes	—
196	C₇×#121	C₂³	1	4	yes	—
197	C₇×#121	C₂³	1	4	yes	—
198	C₇×#121	C₂³	1	16	yes	—
199	C₇×#121	C₂³	1	8	yes	—
200	C₇×#121	C₂³	1	8	yes	—
201	C₇×#121	C₂³	1	8	yes	—
202	C₇×#121	C₂³	1	16	yes	complemented
203	C₇×#121	C₂³	1	8	yes	complemented
204	C₇×#121	C₂³	1	8	yes	complemented
205	C₇×#121	C₂³	1	16	yes	complemented
206	C₇×#121	C₂³	1	8	yes	complemented
207	C₇×#121	C₂³	1	8	yes	complemented
208	C₇×#121	C₂³	1	8	yes	complemented
209	C₇×#120	C₂³	1	8	yes	—
210	C₇×#120	C₂³	1	16	yes	—
211	C₇×#120	C₂³	1	16	yes	—
212	C₇×#120	C₂³	1	16	yes	—
213	C₇×#120	C₂³	1	16	yes	—
214	C₇×#120	C₂³	1	16	yes	complemented
215	C₄×C₇×Q₈	C₂³	1	4	yes	complemented
216	C₄×C₇×Q₈	C₂³	1	4	yes	complemented
217	C₄×C₇×Q₈	C₂³	1	8	yes	complemented
218	C₄×C₇×Q₈	C₂³	1	8	yes	complemented
219	C₄×C₇×Q₈	C₂³	1	4	yes	complemented
220	C₄×C₇×Q₈	C₂³	1	4	yes	complemented
221	C₄×C₇×D₄	C₂³	1	8	yes	—
222	C₄×C₇×D₄	C₂³	1	4	yes	—
223	C₄×C₇×D₄	C₂³	1	4	yes	—
224	C₄×C₇×D₄	C₂³	1	8	yes	—
225	C₄×C₇×D₄	C₂³	1	8	yes	—
226	C₄×C₇×D₄	C₂³	1	16	yes	—
227	C₄×C₇×D₄	C₂³	1	8	yes	—
228	C₄×C₇×D₄	C₂³	1	8	yes	—
229	C₄×C₇×D₄	C₂³	1	4	yes	—
230	C₄×C₇×D₄	C₂³	1	8	yes	—
231	C₄×C₇×D₄	C₂³	1	4	yes	—
232	C₄×C₇×D₄	C₂³	1	16	yes	—
233	C₄×C₇×D₄	C₂³	1	8	yes	—
234	C₄×C₇×D₄	C₂³	1	8	yes	—
235	C₄×C₇×D₄	C₂³	1	8	yes	—
236	C₄×C₇×D₄	C₂³	1	8	yes	—
237	C₄×C₇×D₄	C₂³	1	16	yes	complemented
238	C₄×C₇×D₄	C₂³	1	4	yes	complemented
239	C₄×C₇×D₄	C₂³	1	16	yes	complemented
240	C₄×C₇×D₄	C₂³	1	16	yes	complemented
241	C₄×C₇×D₄	C₂³	1	8	yes	complemented
242	C₄×C₇×D₄	C₂³	1	4	yes	complemented
243	C₄×C₇×D₄	C₂³	1	16	yes	complemented
244	C₄×C₇×D₄	C₂³	1	16	yes	complemented
245	C₄×C₇×D₄	C₂³	1	8	yes	complemented
246	C₄×C₇×D₄	C₂³	1	16	yes	complemented
247	C₄×C₇×D₄	C₂³	1	4	yes	complemented
248	C₄×C₇×D₄	C₂³	1	4	yes	complemented
249	C₇×#117	C₂³	1	4	yes	—
250	C₇×#117	C₂³	1	4	yes	—
251	C₇×#117	C₂³	1	8	yes	—
252	C₇×#117	C₂³	1	4	yes	—
253	C₇×#117	C₂³	1	8	yes	complemented
254	C₇×#117	C₂³	1	16	yes	complemented
255	C₇×#117	C₂³	1	8	yes	complemented
256	C₇×#117	C₂³	1	8	yes	complemented
257	C₇×#117	C₂³	1	8	yes	complemented
258	C₇×#117	C₂³	1	16	yes	complemented
259	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
260	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
261	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
262	C₂×C₇×C₄⋊C₄	C₂³	1	1	yes	characteristic
263	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	complemented
264	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	complemented
265	C₂×C₇×C₄⋊C₄	C₂³	1	8	yes	complemented
266	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
267	C₂×C₇×C₄⋊C₄	C₂³	1	4	yes	complemented
268	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
269	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
270	C₂×C₇×C₂²⋊C₄	C₂³	1	1	yes	characteristic
271	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
272	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
273	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
274	C₂×C₇×C₂²⋊C₄	C₂³	1	2	yes	—
275	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
276	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
277	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	—
278	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
279	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
280	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	—
281	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	complemented
282	C₂×C₇×C₂²⋊C₄	C₂³	1	16	yes	complemented
283	C₂×C₇×C₂²⋊C₄	C₂³	1	8	yes	complemented
284	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
285	C₂×C₄²×C₇	C₂³	1	1	yes	characteristic
286	C₂×C₄²×C₇	C₂³	1	2	yes	—
287	C₂×C₄²×C₇	C₂³	1	8	yes	complemented
288	C₂×C₄²×C₇	C₂³	1	8	yes	complemented
289	#3521	C₂×C₇	1	8	yes	complemented
290	#3519	C₂×C₇	1	8	yes	complemented
291	#3514	C₂×C₇	1	8	yes	complemented
292	#3513	C₂×C₇	1	8	yes	complemented
293	#3506	C₂×C₇	1	2	yes	complemented
294	#3505	C₂×C₇	1	4	yes	complemented
295	#3501	C₂×C₇	1	1	yes	characteristic, complemented
296	#3496	C₂×C₇	1	1	yes	characteristic, complemented
297	#3493	C₂×C₇	1	2	yes	complemented
298	#3490	C₂×C₇	1	4	yes	complemented
299	#3484	C₂×C₇	1	2	yes	complemented
300	#3460	C₂×C₇	1	2	yes	complemented
301	#3459	C₂×C₇	1	4	yes	complemented
302	#3455	C₂×C₇	1	2	yes	complemented
303	C₂×#538	C₂×C₇	1	4	yes	complemented
304	C₄×H(5,𝔽₂)	C₂×C₇	1	2	yes	complemented
305	C₂×#518	C₂×C₇	1	1	yes	characteristic, complemented
306	C₂⁴×C₇	—	2	8	no	—
307	C₂⁴×C₇	—	8	2	no	—
308	C₂⁴×C₇	—	8	2	no	—
309	C₂⁴×C₇	C₂⁴	1	8	yes	—
310	C₂⁴×C₇	C₂⁴	1	1	yes	characteristic
311	C₂⁴×C₇	C₂⁴	1	2	yes	—
312	C₂⁴×C₇	C₂⁴	1	8	yes	—
313	C₂⁴×C₇	C₂⁴	1	2	yes	—
314	C₇×#41	—	2	32	no	—
315	C₇×#41	—	2	16	no	—
316	C₇×#41	—	8	8	no	—
317	C₇×#41	—	8	8	no	—
318	C₂×C₇×Q₈	—	8	4	no	—
319	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
320	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
321	C₂×C₇×Q₈	C₂⁴	1	4	yes	—
322	C₂×C₇×Q₈	C₂⁴	1	8	yes	—
323	C₂×C₇×D₄	—	2	8	no	—
324	C₂×C₇×D₄	—	2	32	no	—
325	C₂×C₇×D₄	—	2	32	no	—
326	C₂×C₇×D₄	—	2	32	no	—
327	C₂×C₇×D₄	—	2	4	no	—
328	C₂×C₇×D₄	—	8	8	no	—
329	C₂×C₇×D₄	—	8	8	no	—
330	C₂×C₇×D₄	—	8	4	no	—
331	C₂×C₇×D₄	#41	1	8	yes	complemented
332	C₂×C₇×D₄	C₂⁴	1	8	yes	—
333	C₂×C₇×D₄	C₂⁴	1	8	yes	—
334	C₂×C₇×D₄	C₂⁴	1	4	yes	—
335	C₂×C₇×D₄	C₂⁴	1	16	yes	—
336	C₂×C₇×D₄	C₂⁴	1	4	yes	—
337	C₂×C₇×D₄	C₂⁴	1	8	yes	—
338	C₂×C₇×D₄	C₂⁴	1	8	yes	—
339	C₂×C₇×D₄	C₂⁴	1	16	yes	—
340	C₂×C₇×D₄	C₂⁴	1	16	yes	—
341	C₂×C₇×D₄	C₂⁴	1	4	yes	—
342	C₂×C₇×D₄	C₂⁴	1	8	yes	—
343	C₂×C₇×D₄	C₂⁴	1	4	yes	—
344	C₂×C₇×D₄	C₂⁴	1	4	yes	—
345	C₂²×C₄×C₇	—	2	4	no	—
346	C₂²×C₄×C₇	—	8	2	no	—
347	C₂²×C₄×C₇	—	8	2	no	—
348	C₂²×C₄×C₇	—	8	2	no	—
349	C₂²×C₄×C₇	—	8	2	no	—
350	C₂²×C₄×C₇	—	8	8	no	—
351	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
352	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
353	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
354	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
355	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
356	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
357	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
358	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
359	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
360	C₂²×C₄×C₇	C₂⁴	1	2	yes	—
361	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
362	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
363	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
364	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
365	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
366	C₂²×C₄×C₇	C₂⁴	1	4	yes	—
367	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
368	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
369	C₂²×C₄×C₇	C₂⁴	1	8	yes	—
370	C₂²×C₄×C₇	C₂⁴	1	16	yes	—
371	C₂²×C₄×C₇	C₂⁴	1	1	yes	characteristic
372	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
373	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
374	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
375	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
376	C₇×C₄⋊C₄	C₂⁴	1	2	yes	—
377	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
378	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
379	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
380	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
381	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
382	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
383	C₇×C₄⋊C₄	C₂⁴	1	16	yes	—
384	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
385	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
386	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
387	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
388	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
389	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
390	C₇×C₄⋊C₄	C₂⁴	1	4	yes	—
391	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
392	C₇×C₄⋊C₄	C₂⁴	1	8	yes	—
393	C₇×C₂²⋊C₄	C₂⁴	1	2	yes	—
394	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
395	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
396	C₇×C₂²⋊C₄	C₂⁴	1	2	yes	—
397	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
398	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
399	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
400	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
401	C₇×C₂²⋊C₄	C₂⁴	1	4	yes	—
402	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
403	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
404	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
405	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
406	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
407	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
408	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
409	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
410	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
411	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
412	C₇×C₂²⋊C₄	C₂⁴	1	16	yes	—
413	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
414	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
415	C₇×C₂²⋊C₄	C₂⁴	1	8	yes	—
416	C₄²×C₇	C₂⁴	1	4	yes	—
417	C₄²×C₇	C₂⁴	1	8	yes	—
418	C₄²×C₇	C₂⁴	1	2	yes	—
419	C₄²×C₇	C₂⁴	1	2	yes	—
420	C₄²×C₇	C₂⁴	1	8	yes	—
421	C₄²×C₇	C₂⁴	1	8	yes	—
422	C₄²×C₇	C₂⁴	1	8	yes	—
423	C₄²×C₇	C₂⁴	1	16	yes	—
424	C₂×H(5,𝔽₂)	C₂²×C₇	1	2	yes	—
425	C₂³×D₄	C₂²×C₇	1	1	yes	characteristic
426	#559	C₂²×C₇	1	8	yes	complemented
427	#556	C₂²×C₇	1	8	yes	complemented
428	#556	C₂²×C₇	1	4	yes	complemented
429	#555	C₂²×C₇	1	8	yes	complemented
430	#555	C₂²×C₇	1	4	yes	complemented
431	#554	C₂²×C₇	1	4	yes	complemented
432	#554	C₂²×C₇	1	8	yes	complemented
433	#553	C₂²×C₇	1	8	yes	complemented
434	#553	C₂²×C₇	1	8	yes	complemented
435	#553	C₂²×C₇	1	16	yes	complemented
436	#553	C₂²×C₇	1	8	yes	complemented
437	#552	C₂²×C₇	1	8	yes	complemented
438	#552	C₂²×C₇	1	8	yes	complemented
439	#551	C₂²×C₇	1	16	yes	complemented
440	#551	C₂²×C₇	1	16	yes	complemented
441	#551	C₂²×C₇	1	16	yes	complemented
442	#550	C₂²×C₇	1	4	yes	complemented
443	D₄×Q₈	C₂²×C₇	1	4	yes	complemented
444	#548	C₂²×C₇	1	8	yes	complemented
445	#547	C₂²×C₇	1	4	yes	complemented
446	#547	C₂²×C₇	1	4	yes	complemented
447	#546	C₂²×C₇	1	8	yes	complemented
448	#546	C₂²×C₇	1	8	yes	complemented
449	#546	C₂²×C₇	1	16	yes	complemented
450	#546	C₂²×C₇	1	16	yes	complemented
451	#546	C₂²×C₇	1	8	yes	complemented
452	#546	C₂²×C₇	1	8	yes	complemented
453	D₄²	C₂²×C₇	1	8	yes	complemented
454	D₄²	C₂²×C₇	1	8	yes	complemented
455	D₄²	C₂²×C₇	1	4	yes	complemented
456	#544	C₂²×C₇	1	2	yes	complemented
457	#543	C₂²×C₇	1	4	yes	complemented
458	#542	C₂²×C₇	1	4	yes	complemented
459	#542	C₂²×C₇	1	4	yes	complemented
460	#542	C₂²×C₇	1	8	yes	complemented
461	#541	C₂²×C₇	1	4	yes	complemented
462	#540	C₂²×C₇	1	4	yes	complemented
463	#540	C₂²×C₇	1	8	yes	complemented
464	#539	C₂²×C₇	1	4	yes	complemented
465	#539	C₂²×C₇	1	4	yes	complemented
466	#539	C₂²×C₇	1	16	yes	complemented
467	#538	C₂²×C₇	1	4	yes	complemented
468	#538	C₂²×C₇	1	8	yes	complemented
469	#538	C₂²×C₇	1	4	yes	complemented
470	#538	C₂²×C₇	1	8	yes	complemented
471	#538	C₂²×C₇	1	8	yes	complemented
472	#538	C₂²×C₇	1	16	yes	complemented
473	#538	C₂²×C₇	1	16	yes	complemented
474	#538	C₂²×C₇	1	16	yes	complemented
475	#537	C₂²×C₇	1	2	yes	complemented
476	#535	C₂²×C₇	1	4	yes	complemented
477	#534	C₂²×C₇	1	8	yes	complemented
478	#534	C₂²×C₇	1	4	yes	complemented
479	#533	C₂²×C₇	1	2	yes	complemented
480	#532	C₂²×C₇	1	2	yes	complemented
481	#532	C₂²×C₇	1	8	yes	complemented
482	#529	C₂²×C₇	1	8	yes	complemented
483	#529	C₂²×C₇	1	8	yes	complemented
484	#529	C₂²×C₇	1	8	yes	complemented
485	#529	C₂²×C₇	1	16	yes	complemented
486	#529	C₂²×C₇	1	8	yes	complemented
487	C₂×#126	C₂²×C₇	1	8	yes	complemented
488	C₂×#124	C₂²×C₇	1	8	yes	complemented
489	#525	C₂²×C₇	1	4	yes	complemented
490	#525	C₂²×C₇	1	8	yes	complemented
491	#525	C₂²×C₇	1	8	yes	complemented
492	#525	C₂²×C₇	1	16	yes	complemented
493	C₂×#123	C₂²×C₇	1	8	yes	complemented
494	C₂×C₂²⋊Q₈	C₂²×C₇	1	4	yes	complemented
495	C₂×#121	C₂²×C₇	1	8	yes	complemented
496	C₂×#121	C₂²×C₇	1	4	yes	complemented
497	C₂×#120	C₂²×C₇	1	8	yes	complemented
498	#520	C₂²×C₇	1	4	yes	complemented
499	#520	C₂²×C₇	1	8	yes	complemented
500	#518	C₂²×C₇	1	2	yes	—
501	#518	C₂²×C₇	1	8	yes	complemented
502	#518	C₂²×C₇	1	8	yes	complemented
503	#518	C₂²×C₇	1	8	yes	complemented
504	#518	C₂²×C₇	1	8	yes	complemented
505	C₄×#41	C₂²×C₇	1	4	yes	complemented
506	C₄×#41	C₂²×C₇	1	8	yes	complemented
507	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
508	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic
509	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
510	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
511	C₂×C₄×D₄	C₂²×C₇	1	2	yes	complemented
512	C₂×C₄×D₄	C₂²×C₇	1	1	yes	characteristic, complemented
513	C₂×C₄×D₄	C₂²×C₇	1	8	yes	complemented
514	C₂×C₄×D₄	C₂²×C₇	1	8	yes	complemented
515	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
516	C₂×#117	C₂²×C₇	1	1	yes	characteristic, complemented
517	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
518	C₂²×C₂²⋊C₄	C₂²×C₇	1	2	yes	complemented
519	C₂³×C₇	—	2	2	no	—
520	C₂³×C₇	—	2	4	no	—
521	C₂³×C₇	—	2	16	no	—
522	C₂³×C₇	—	2	16	no	—
523	C₂³×C₇	—	4	2	no	—
524	C₂³×C₇	—	4	2	no	—
525	C₂³×C₇	—	4	2	no	—
526	C₂³×C₇	—	4	2	no	—
527	C₂³×C₇	—	4	1	no	—
528	C₂³×C₇	—	4	1	no	—
529	C₂³×C₇	—	4	8	no	—
530	C₂³×C₇	—	4	8	no	—
531	C₂³×C₇	—	4	8	no	—
532	C₂³×C₇	—	4	8	no	—
533	C₂³×C₇	—	8	16	no	—
534	C₂³×C₇	C₂×#41	1	8	yes	—
535	C₂³×C₇	C₂⁵	1	2	yes	—
536	C₂³×C₇	C₂⁵	1	4	yes	—
537	C₂³×C₇	C₂⁵	1	8	yes	—
538	C₂³×C₇	C₂⁵	1	4	yes	—
539	C₂³×C₇	C₂⁵	1	1	yes	characteristic
540	C₇×Q₈	—	2	8	no	—
541	C₇×Q₈	—	4	4	no	—
542	C₇×Q₈	—	4	8	no	—
543	C₇×Q₈	—	4	4	no	—
544	C₇×D₄	—	2	16	no	—
545	C₇×D₄	—	2	32	no	—
546	C₇×D₄	—	2	16	no	—
547	C₇×D₄	—	2	8	no	—
548	C₇×D₄	—	2	8	no	—
549	C₇×D₄	—	4	4	no	—
550	C₇×D₄	—	4	8	no	—
551	C₇×D₄	—	4	8	no	—
552	C₇×D₄	—	4	16	no	—
553	C₇×D₄	—	4	8	no	—
554	C₇×D₄	—	4	16	no	—
555	C₇×D₄	—	4	4	no	—
556	C₇×D₄	C₂×#41	1	16	yes	—
557	C₂×C₄×C₇	—	2	2	no	—
558	C₂×C₄×C₇	—	2	16	no	—
559	C₂×C₄×C₇	—	2	8	no	—
560	C₂×C₄×C₇	—	2	16	no	—
561	C₂×C₄×C₇	—	4	1	no	—
562	C₂×C₄×C₇	—	4	2	no	—
563	C₂×C₄×C₇	—	4	1	no	—
564	C₂×C₄×C₇	—	4	8	no	—
565	C₂×C₄×C₇	—	4	8	no	—
566	C₂×C₄×C₇	—	4	1	no	—
567	C₂×C₄×C₇	—	4	2	no	—
568	C₂×C₄×C₇	—	4	1	no	—
569	C₂×C₄×C₇	—	4	4	no	—
570	C₂×C₄×C₇	—	4	8	no	—
571	C₂×C₄×C₇	—	4	4	no	—
572	C₂×C₄×C₇	—	4	16	no	—
573	C₂×C₄×C₇	—	4	8	no	—
574	C₂×C₄×C₇	—	4	8	no	—
575	C₂×C₄×C₇	—	4	8	no	—
576	C₂×C₄×C₇	—	4	8	no	—
577	C₂×C₄×C₇	C₂×#41	1	4	yes	—
578	C₂×C₄×C₇	C₂⁵	1	2	yes	—
579	C₂×C₄×C₇	C₂⁵	1	2	yes	—
580	C₂×C₄×C₇	C₂⁵	1	4	yes	—
581	C₂×C₄×C₇	C₂⁵	1	8	yes	—
582	C₂×C₄×C₇	C₂⁵	1	8	yes	—
583	C₂×C₄×C₇	C₂⁵	1	2	yes	—
584	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
585	C₂×C₄×C₇	C₂⁵	1	4	yes	—
586	C₂×C₄×C₇	C₂⁵	1	2	yes	—
587	C₂×C₄×C₇	C₂⁵	1	8	yes	—
588	C₂×C₄×C₇	C₂⁵	1	1	yes	characteristic
589	C₂×C₄×C₇	C₂⁵	1	2	yes	—
590	C₂⁵	C₂³×C₇	1	2	yes	—
591	H(5,𝔽₂)	—	2	16	no	—
592	C₂×#41	C₂³×C₇	1	4	yes	—
593	C₂×#41	C₂³×C₇	1	8	yes	—
594	C₂×#41	C₂³×C₇	1	8	yes	complemented
595	C₂×#41	C₂³×C₇	1	8	yes	complemented
596	C₂²×Q₈	C₂³×C₇	1	4	yes	complemented
597	C₂²×D₄	—	2	8	no	—
598	C₂²×D₄	C₂³×C₇	1	2	yes	—
599	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
600	C₂²×D₄	C₂³×C₇	1	8	yes	—
601	C₂²×D₄	C₂³×C₇	1	8	yes	—
602	C₂²×D₄	C₂³×C₇	1	8	yes	—
603	C₂²×D₄	C₂³×C₇	1	8	yes	—
604	C₂²×D₄	C₂³×C₇	1	8	yes	—
605	C₂²×D₄	C₂³×C₇	1	1	yes	characteristic
606	C₂²×D₄	C₂³×C₇	1	4	yes	complemented
607	C₂³×C₄	C₂³×C₇	1	1	yes	characteristic
608	C₂³×C₄	C₂³×C₇	1	2	yes	—
609	C₂³×C₄	C₂³×C₇	1	2	yes	—
610	C₂³×C₄	C₂³×C₇	1	2	yes	—
611	C₂³×C₄	C₂³×C₇	1	2	yes	—
612	C₂³×C₄	C₂³×C₇	1	8	yes	complemented
613	C₄⋊Q₈	C₂³×C₇	1	2	yes	complemented
614	C₄⋊Q₈	C₂³×C₇	1	8	yes	complemented
615	C₄⋊Q₈	C₂³×C₇	1	2	yes	complemented
616	C₄⋊Q₈	C₂³×C₇	1	2	yes	complemented
617	#127	C₂³×C₇	1	8	yes	—
618	#127	C₂³×C₇	1	2	yes	complemented
619	#126	C₂³×C₇	1	8	yes	—
620	#126	C₂³×C₇	1	16	yes	—
621	#126	C₂³×C₇	1	8	yes	—
622	#126	C₂³×C₇	1	16	yes	complemented
623	#126	C₂³×C₇	1	16	yes	complemented
624	#126	C₂³×C₇	1	8	yes	complemented
625	#126	C₂³×C₇	1	16	yes	complemented
626	#126	C₂³×C₇	1	8	yes	complemented
627	#125	C₂³×C₇	1	8	yes	complemented
628	#125	C₂³×C₇	1	8	yes	complemented
629	#125	C₂³×C₇	1	8	yes	complemented
630	#125	C₂³×C₇	1	8	yes	complemented
631	#125	C₂³×C₇	1	4	yes	complemented
632	#124	C₂³×C₇	1	8	yes	—
633	#124	C₂³×C₇	1	16	yes	—
634	#124	C₂³×C₇	1	8	yes	—
635	#124	C₂³×C₇	1	8	yes	—
636	#124	C₂³×C₇	1	16	yes	complemented
637	#124	C₂³×C₇	1	16	yes	complemented
638	#124	C₂³×C₇	1	8	yes	complemented
639	#124	C₂³×C₇	1	4	yes	complemented
640	#123	C₂³×C₇	1	8	yes	—
641	#123	C₂³×C₇	1	16	yes	—
642	#123	C₂³×C₇	1	8	yes	—
643	#123	C₂³×C₇	1	16	yes	—
644	#123	C₂³×C₇	1	8	yes	—
645	#123	C₂³×C₇	1	16	yes	complemented
646	#123	C₂³×C₇	1	16	yes	complemented
647	#123	C₂³×C₇	1	8	yes	complemented
648	#123	C₂³×C₇	1	16	yes	complemented
649	#123	C₂³×C₇	1	16	yes	complemented
650	#123	C₂³×C₇	1	16	yes	complemented
651	#123	C₂³×C₇	1	8	yes	complemented
652	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
653	C₂²⋊Q₈	C₂³×C₇	1	8	yes	—
654	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
655	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
656	C₂²⋊Q₈	C₂³×C₇	1	4	yes	—
657	C₂²⋊Q₈	C₂³×C₇	1	8	yes	complemented
658	C₂²⋊Q₈	C₂³×C₇	1	8	yes	complemented
659	C₂²⋊Q₈	C₂³×C₇	1	8	yes	complemented
660	C₂²⋊Q₈	C₂³×C₇	1	8	yes	complemented
661	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
662	C₂²⋊Q₈	C₂³×C₇	1	8	yes	complemented
663	C₂²⋊Q₈	C₂³×C₇	1	8	yes	complemented
664	C₂²⋊Q₈	C₂³×C₇	1	16	yes	complemented
665	C₂²⋊Q₈	C₂³×C₇	1	8	yes	complemented
666	#121	C₂³×C₇	1	8	yes	—
667	#121	C₂³×C₇	1	4	yes	—
668	#121	C₂³×C₇	1	8	yes	—
669	#121	C₂³×C₇	1	16	yes	—
670	#121	C₂³×C₇	1	4	yes	—
671	#121	C₂³×C₇	1	16	yes	—
672	#121	C₂³×C₇	1	4	yes	—
673	#121	C₂³×C₇	1	4	yes	—
674	#121	C₂³×C₇	1	16	yes	—
675	#121	C₂³×C₇	1	8	yes	—
676	#121	C₂³×C₇	1	8	yes	—
677	#121	C₂³×C₇	1	8	yes	—
678	#121	C₂³×C₇	1	16	yes	complemented
679	#121	C₂³×C₇	1	8	yes	complemented
680	#121	C₂³×C₇	1	8	yes	complemented
681	#121	C₂³×C₇	1	16	yes	complemented
682	#121	C₂³×C₇	1	8	yes	complemented
683	#121	C₂³×C₇	1	8	yes	complemented
684	#121	C₂³×C₇	1	8	yes	complemented
685	#120	C₂³×C₇	1	8	yes	—
686	#120	C₂³×C₇	1	16	yes	—
687	#120	C₂³×C₇	1	16	yes	—
688	#120	C₂³×C₇	1	16	yes	—
689	#120	C₂³×C₇	1	16	yes	—
690	#120	C₂³×C₇	1	16	yes	complemented
691	C₄×Q₈	C₂³×C₇	1	4	yes	complemented
692	C₄×Q₈	C₂³×C₇	1	4	yes	complemented
693	C₄×Q₈	C₂³×C₇	1	8	yes	complemented
694	C₄×Q₈	C₂³×C₇	1	8	yes	complemented
695	C₄×Q₈	C₂³×C₇	1	4	yes	complemented
696	C₄×Q₈	C₂³×C₇	1	4	yes	complemented
697	C₄×D₄	C₂³×C₇	1	8	yes	—
698	C₄×D₄	C₂³×C₇	1	4	yes	—
699	C₄×D₄	C₂³×C₇	1	4	yes	—
700	C₄×D₄	C₂³×C₇	1	8	yes	—
701	C₄×D₄	C₂³×C₇	1	8	yes	—
702	C₄×D₄	C₂³×C₇	1	16	yes	—
703	C₄×D₄	C₂³×C₇	1	8	yes	—
704	C₄×D₄	C₂³×C₇	1	8	yes	—
705	C₄×D₄	C₂³×C₇	1	4	yes	—
706	C₄×D₄	C₂³×C₇	1	8	yes	—
707	C₄×D₄	C₂³×C₇	1	4	yes	—
708	C₄×D₄	C₂³×C₇	1	16	yes	—
709	C₄×D₄	C₂³×C₇	1	8	yes	—
710	C₄×D₄	C₂³×C₇	1	8	yes	—
711	C₄×D₄	C₂³×C₇	1	8	yes	—
712	C₄×D₄	C₂³×C₇	1	8	yes	—
713	C₄×D₄	C₂³×C₇	1	16	yes	complemented
714	C₄×D₄	C₂³×C₇	1	4	yes	complemented
715	C₄×D₄	C₂³×C₇	1	16	yes	complemented
716	C₄×D₄	C₂³×C₇	1	16	yes	complemented
717	C₄×D₄	C₂³×C₇	1	8	yes	complemented
718	C₄×D₄	C₂³×C₇	1	4	yes	complemented
719	C₄×D₄	C₂³×C₇	1	16	yes	complemented
720	C₄×D₄	C₂³×C₇	1	16	yes	complemented
721	C₄×D₄	C₂³×C₇	1	8	yes	complemented
722	C₄×D₄	C₂³×C₇	1	16	yes	complemented
723	C₄×D₄	C₂³×C₇	1	4	yes	complemented
724	C₄×D₄	C₂³×C₇	1	4	yes	complemented
725	#117	C₂³×C₇	1	4	yes	—
726	#117	C₂³×C₇	1	4	yes	—
727	#117	C₂³×C₇	1	8	yes	—
728	#117	C₂³×C₇	1	4	yes	—
729	#117	C₂³×C₇	1	8	yes	complemented
730	#117	C₂³×C₇	1	16	yes	complemented
731	#117	C₂³×C₇	1	8	yes	complemented
732	#117	C₂³×C₇	1	8	yes	complemented
733	#117	C₂³×C₇	1	8	yes	complemented
734	#117	C₂³×C₇	1	16	yes	complemented
735	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
736	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
737	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
738	C₂×C₄⋊C₄	C₂³×C₇	1	1	yes	characteristic
739	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	complemented
740	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	complemented
741	C₂×C₄⋊C₄	C₂³×C₇	1	8	yes	complemented
742	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
743	C₂×C₄⋊C₄	C₂³×C₇	1	4	yes	complemented
744	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
745	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
746	C₂×C₂²⋊C₄	C₂³×C₇	1	1	yes	characteristic
747	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
748	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
749	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
750	C₂×C₂²⋊C₄	C₂³×C₇	1	2	yes	—
751	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
752	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
753	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	—
754	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
755	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
756	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	—
757	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	complemented
758	C₂×C₂²⋊C₄	C₂³×C₇	1	16	yes	complemented
759	C₂×C₂²⋊C₄	C₂³×C₇	1	8	yes	complemented
760	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
761	C₂×C₄²	C₂³×C₇	1	1	yes	characteristic
762	C₂×C₄²	C₂³×C₇	1	2	yes	—
763	C₂×C₄²	C₂³×C₇	1	8	yes	complemented
764	C₂×C₄²	C₂³×C₇	1	8	yes	complemented
765	C₂²×C₇	—	2	1	no	—
766	C₂²×C₇	—	2	1	no	—
767	C₂²×C₇	—	2	4	no	—
768	C₂²×C₇	—	2	4	no	—
769	C₂²×C₇	—	2	2	no	—
770	C₂²×C₇	—	2	8	no	—
771	C₂²×C₇	—	2	4	no	—
772	C₂²×C₇	—	2	8	no	—
773	C₂²×C₇	—	2	4	no	—
774	C₂²×C₇	—	2	4	no	—
775	C₂²×C₇	—	2	8	no	—
776	C₂²×C₇	—	2	2	no	—
777	C₂²×C₇	—	2	2	no	—
778	C₂²×C₇	—	4	8	no	—
779	C₂²×C₇	—	4	8	no	—
780	C₂²×C₇	—	4	4	no	—
781	C₂²×C₇	—	8	16	no	—
782	C₂²×C₇	—	8	16	no	—
783	C₂²×C₇	C₂²×#41	1	8	yes	—
784	C₂²×C₇	C₂²×#41	1	2	yes	—
785	C₂²×C₇	C₂⁶	1	1	yes	characteristic
786	C₄×C₇	—	2	2	no	—
787	C₄×C₇	—	2	8	no	—
788	C₄×C₇	—	2	2	no	—
789	C₄×C₇	—	2	4	no	—
790	C₄×C₇	—	2	2	no	—
791	C₄×C₇	—	2	1	no	—
792	C₄×C₇	—	2	8	no	—
793	C₄×C₇	—	2	4	no	—
794	C₄×C₇	—	2	2	no	—
795	C₄×C₇	—	2	1	no	—
796	C₄×C₇	—	2	8	no	—
797	C₄×C₇	C₂²×#41	1	4	yes	—
798	C₂⁴	—	2	8	no	—
799	C₂⁴	—	8	2	no	—
800	C₂⁴	—	8	2	no	—
801	C₂⁴	C₂⁴×C₇	1	8	yes	—
802	C₂⁴	C₂⁴×C₇	1	1	yes	characteristic
803	C₂⁴	C₂⁴×C₇	1	2	yes	—
804	C₂⁴	C₂⁴×C₇	1	8	yes	—
805	C₂⁴	C₂⁴×C₇	1	2	yes	—
806	#41	—	2	32	no	—
807	#41	—	2	16	no	—
808	#41	—	8	8	no	—
809	#41	—	8	8	no	—
810	C₂×Q₈	—	8	4	no	—
811	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
812	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
813	C₂×Q₈	C₂⁴×C₇	1	4	yes	—
814	C₂×Q₈	C₂⁴×C₇	1	8	yes	—
815	C₂×D₄	—	2	8	no	—
816	C₂×D₄	—	2	32	no	—
817	C₂×D₄	—	2	32	no	—
818	C₂×D₄	—	2	32	no	—
819	C₂×D₄	—	2	4	no	—
820	C₂×D₄	—	8	8	no	—
821	C₂×D₄	—	8	8	no	—
822	C₂×D₄	—	8	4	no	—
823	C₂×D₄	C₇×#41	1	8	yes	complemented
824	C₂×D₄	C₂⁴×C₇	1	8	yes	—
825	C₂×D₄	C₂⁴×C₇	1	8	yes	—
826	C₂×D₄	C₂⁴×C₇	1	4	yes	—
827	C₂×D₄	C₂⁴×C₇	1	16	yes	—
828	C₂×D₄	C₂⁴×C₇	1	4	yes	—
829	C₂×D₄	C₂⁴×C₇	1	8	yes	—
830	C₂×D₄	C₂⁴×C₇	1	8	yes	—
831	C₂×D₄	C₂⁴×C₇	1	16	yes	—
832	C₂×D₄	C₂⁴×C₇	1	16	yes	—
833	C₂×D₄	C₂⁴×C₇	1	4	yes	—
834	C₂×D₄	C₂⁴×C₇	1	8	yes	—
835	C₂×D₄	C₂⁴×C₇	1	4	yes	—
836	C₂×D₄	C₂⁴×C₇	1	4	yes	—
837	C₂²×C₄	—	2	4	no	—
838	C₂²×C₄	—	8	2	no	—
839	C₂²×C₄	—	8	2	no	—
840	C₂²×C₄	—	8	2	no	—
841	C₂²×C₄	—	8	2	no	—
842	C₂²×C₄	—	8	8	no	—
843	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
844	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
845	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
846	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
847	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
848	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
849	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
850	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
851	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
852	C₂²×C₄	C₂⁴×C₇	1	2	yes	—
853	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
854	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
855	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
856	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
857	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
858	C₂²×C₄	C₂⁴×C₇	1	4	yes	—
859	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
860	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
861	C₂²×C₄	C₂⁴×C₇	1	8	yes	—
862	C₂²×C₄	C₂⁴×C₇	1	16	yes	—
863	C₂²×C₄	C₂⁴×C₇	1	1	yes	characteristic
864	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
865	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
866	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
867	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
868	C₄⋊C₄	C₂⁴×C₇	1	2	yes	—
869	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
870	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
871	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
872	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
873	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
874	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
875	C₄⋊C₄	C₂⁴×C₇	1	16	yes	—
876	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
877	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
878	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
879	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
880	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
881	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
882	C₄⋊C₄	C₂⁴×C₇	1	4	yes	—
883	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
884	C₄⋊C₄	C₂⁴×C₇	1	8	yes	—
885	C₂²⋊C₄	C₂⁴×C₇	1	2	yes	—
886	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
887	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
888	C₂²⋊C₄	C₂⁴×C₇	1	2	yes	—
889	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
890	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
891	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
892	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
893	C₂²⋊C₄	C₂⁴×C₇	1	4	yes	—
894	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
895	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
896	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
897	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
898	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
899	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
900	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
901	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
902	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
903	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
904	C₂²⋊C₄	C₂⁴×C₇	1	16	yes	—
905	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
906	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
907	C₂²⋊C₄	C₂⁴×C₇	1	8	yes	—
908	C₄²	C₂⁴×C₇	1	4	yes	—
909	C₄²	C₂⁴×C₇	1	8	yes	—
910	C₄²	C₂⁴×C₇	1	2	yes	—
911	C₄²	C₂⁴×C₇	1	2	yes	—
912	C₄²	C₂⁴×C₇	1	8	yes	—
913	C₄²	C₂⁴×C₇	1	8	yes	—
914	C₄²	C₂⁴×C₇	1	8	yes	—
915	C₄²	C₂⁴×C₇	1	16	yes	—
916	C₂×C₇	—	2	2	no	—
917	C₂×C₇	—	2	8	no	—
918	C₂×C₇	—	4	4	no	—
919	C₂×C₇	—	4	2	no	—
920	C₂×C₇	—	4	8	no	—
921	C₂×C₇	C₂³×#41	1	1	yes	characteristic
922	C₂×C₇	H(7,𝔽₂)	1	1	yes	characteristic
923	C₂×C₇	H(7,𝔽₂)	1	1	yes	characteristic
924	C₂³	—	2	2	no	—
925	C₂³	—	2	4	no	—
926	C₂³	—	2	16	no	—
927	C₂³	—	2	16	no	—
928	C₂³	—	4	2	no	—
929	C₂³	—	4	2	no	—
930	C₂³	—	4	2	no	—
931	C₂³	—	4	2	no	—
932	C₂³	—	4	1	no	—
933	C₂³	—	4	1	no	—
934	C₂³	—	4	8	no	—
935	C₂³	—	4	8	no	—
936	C₂³	—	4	8	no	—
937	C₂³	—	4	8	no	—
938	C₂³	—	8	16	no	—
939	C₂³	C₂×C₇×#41	1	8	yes	—
940	C₂³	C₂⁵×C₇	1	2	yes	—
941	C₂³	C₂⁵×C₇	1	4	yes	—
942	C₂³	C₂⁵×C₇	1	8	yes	—
943	C₂³	C₂⁵×C₇	1	4	yes	—
944	C₂³	C₂⁵×C₇	1	1	yes	characteristic
945	Q₈	—	2	8	no	—
946	Q₈	—	4	4	no	—
947	Q₈	—	4	8	no	—
948	Q₈	—	4	4	no	—
949	D₄	—	2	16	no	—
950	D₄	—	2	32	no	—
951	D₄	—	2	16	no	—
952	D₄	—	2	8	no	—
953	D₄	—	2	8	no	—
954	D₄	—	4	4	no	—
955	D₄	—	4	8	no	—
956	D₄	—	4	8	no	—
957	D₄	—	4	16	no	—
958	D₄	—	4	8	no	—
959	D₄	—	4	16	no	—
960	D₄	—	4	4	no	—
961	D₄	C₂×C₇×#41	1	16	yes	—
962	C₂×C₄	—	2	2	no	—
963	C₂×C₄	—	2	16	no	—
964	C₂×C₄	—	2	8	no	—
965	C₂×C₄	—	2	16	no	—
966	C₂×C₄	—	4	1	no	—
967	C₂×C₄	—	4	2	no	—
968	C₂×C₄	—	4	1	no	—
969	C₂×C₄	—	4	8	no	—
970	C₂×C₄	—	4	8	no	—
971	C₂×C₄	—	4	1	no	—
972	C₂×C₄	—	4	2	no	—
973	C₂×C₄	—	4	1	no	—
974	C₂×C₄	—	4	4	no	—
975	C₂×C₄	—	4	8	no	—
976	C₂×C₄	—	4	4	no	—
977	C₂×C₄	—	4	16	no	—
978	C₂×C₄	—	4	8	no	—
979	C₂×C₄	—	4	8	no	—
980	C₂×C₄	—	4	8	no	—
981	C₂×C₄	—	4	8	no	—
982	C₂×C₄	C₂×C₇×#41	1	4	yes	—
983	C₂×C₄	C₂⁵×C₇	1	2	yes	—
984	C₂×C₄	C₂⁵×C₇	1	2	yes	—
985	C₂×C₄	C₂⁵×C₇	1	4	yes	—
986	C₂×C₄	C₂⁵×C₇	1	8	yes	—
987	C₂×C₄	C₂⁵×C₇	1	8	yes	—
988	C₂×C₄	C₂⁵×C₇	1	2	yes	—
989	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
990	C₂×C₄	C₂⁵×C₇	1	4	yes	—
991	C₂×C₄	C₂⁵×C₇	1	2	yes	—
992	C₂×C₄	C₂⁵×C₇	1	8	yes	—
993	C₂×C₄	C₂⁵×C₇	1	1	yes	characteristic
994	C₂×C₄	C₂⁵×C₇	1	2	yes	—
995	C₇	#62846	1	1	yes	characteristic, direct product factor, Sylow
996	C₂²	—	2	1	no	—
997	C₂²	—	2	1	no	—
998	C₂²	—	2	4	no	—
999	C₂²	—	2	4	no	—
1000	C₂²	—	2	2	no	—
1001	C₂²	—	2	8	no	—
1002	C₂²	—	2	4	no	—
1003	C₂²	—	2	8	no	—
1004	C₂²	—	2	4	no	—
1005	C₂²	—	2	4	no	—
1006	C₂²	—	2	8	no	—
1007	C₂²	—	2	2	no	—
1008	C₂²	—	2	2	no	—
1009	C₂²	—	4	8	no	—
1010	C₂²	—	4	4	no	—
1011	C₂²	—	4	8	no	—
1012	C₂²	—	8	16	no	—
1013	C₂²	—	8	16	no	—
1014	C₂²	C₂²×C₇×#41	1	8	yes	—
1015	C₂²	C₂²×C₇×#41	1	2	yes	—
1016	C₂²	C₂⁶×C₇	1	1	yes	characteristic
1017	C₄	—	2	2	no	—
1018	C₄	—	2	8	no	—
1019	C₄	—	2	2	no	—
1020	C₄	—	2	4	no	—
1021	C₄	—	2	2	no	—
1022	C₄	—	2	1	no	—
1023	C₄	—	2	8	no	—
1024	C₄	—	2	4	no	—
1025	C₄	—	2	2	no	—
1026	C₄	—	2	1	no	—
1027	C₄	—	2	8	no	—
1028	C₄	C₂²×C₇×#41	1	4	yes	—
1029	C₂	—	2	2	no	—
1030	C₂	—	2	8	no	—
1031	C₂	—	4	2	no	—
1032	C₂	—	4	4	no	—
1033	C₂	—	4	8	no	—
1034	C₂	C₂³×C₇×#41	1	1	yes	characteristic
1035	C₂	C₇×H(7,𝔽₂)	1	1	yes	characteristic
1036	C₂	C₇×H(7,𝔽₂)	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₇	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₇
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₇×#3521	C₂	semidirect
2. C₇×#3519	C₂	semidirect
3. C₇×#3514	C₂	semidirect
4. C₇×#3513	C₂	semidirect
5. C₇×#3506	C₂	semidirect
6. C₇×#3505	C₂	semidirect
7. C₇×#3501	C₂	semidirect
8. C₇×#3496	C₂	semidirect
9. C₇×#3493	C₂	semidirect
10. C₇×#3490	C₂	semidirect
11. C₇×#3484	C₂	semidirect
12. C₇×#3460	C₂	semidirect
13. C₇×#3459	C₂	semidirect
14. C₇×#3455	C₂	semidirect
15. C₂×C₇×#538	C₂	semidirect
16. C₄×C₇×H(5,𝔽₂)	C₂	semidirect
17. C₂×C₇×#518	C₂	semidirect
20. C₇×#559	C₂²	semidirect
21. C₇×#556	C₂²	semidirect
22. C₇×#556	C₂²	semidirect
23. C₇×#555	C₂²	semidirect
24. C₇×#555	C₂²	semidirect
25. C₇×#554	C₂²	semidirect
26. C₇×#554	C₂²	semidirect
27. C₇×#553	C₂²	semidirect
28. C₇×#553	C₂²	semidirect
29. C₇×#553	C₂²	semidirect
30. C₇×#553	C₂²	semidirect
31. C₇×#552	C₂²	semidirect
32. C₇×#552	C₂²	semidirect
33. C₇×#551	C₂²	semidirect
34. C₇×#551	C₂²	semidirect
35. C₇×#551	C₂²	semidirect
36. C₇×#550	C₂²	semidirect
37. C₇×D₄×Q₈	C₂²	semidirect
38. C₇×#548	C₂²	semidirect
39. C₇×#547	C₂²	semidirect
40. C₇×#547	C₂²	semidirect
41. C₇×#546	C₂²	semidirect
42. C₇×#546	C₂²	semidirect
43. C₇×#546	C₂²	semidirect
44. C₇×#546	C₂²	semidirect
45. C₇×#546	C₂²	semidirect
46. C₇×#546	C₂²	semidirect
47. C₇×D₄²	C₂²	semidirect
48. C₇×D₄²	C₂²	semidirect
49. C₇×D₄²	C₂²	semidirect
50. C₇×#544	C₂²	semidirect
51. C₇×#543	C₂²	semidirect
52. C₇×#542	C₂²	semidirect
53. C₇×#542	C₂²	semidirect
54. C₇×#542	C₂²	semidirect
55. C₇×#541	C₂²	semidirect
56. C₇×#540	C₂²	semidirect
57. C₇×#540	C₂²	semidirect
58. C₇×#539	C₂²	semidirect
59. C₇×#539	C₂²	semidirect
60. C₇×#539	C₂²	semidirect
61. C₇×#538	C₂²	semidirect
62. C₇×#538	C₂²	semidirect
63. C₇×#538	C₂²	semidirect
64. C₇×#538	C₂²	semidirect
65. C₇×#538	C₂²	semidirect
66. C₇×#538	C₂²	semidirect
67. C₇×#538	C₂²	semidirect
68. C₇×#538	C₂²	semidirect
69. C₇×#537	C₂²	semidirect
70. C₇×#535	C₂²	semidirect
71. C₇×#534	C₂²	semidirect
72. C₇×#534	C₂²	semidirect
73. C₇×#533	C₂²	semidirect
74. C₇×#532	C₂²	semidirect
75. C₇×#532	C₂²	semidirect
76. C₇×#529	C₂²	semidirect
77. C₇×#529	C₂²	semidirect
78. C₇×#529	C₂²	semidirect
79. C₇×#529	C₂²	semidirect
80. C₇×#529	C₂²	semidirect
81. C₂×C₇×#126	C₂²	semidirect
82. C₂×C₇×#124	C₂²	semidirect
83. C₇×#525	C₂²	semidirect
84. C₇×#525	C₂²	semidirect
85. C₇×#525	C₂²	semidirect
86. C₇×#525	C₂²	semidirect
87. C₂×C₇×#123	C₂²	semidirect
88. C₂×C₇×C₂²⋊Q₈	C₂²	semidirect
89. C₂×C₇×#121	C₂²	semidirect
90. C₂×C₇×#121	C₂²	semidirect
91. C₂×C₇×#120	C₂²	semidirect
92. C₇×#520	C₂²	semidirect
93. C₇×#520	C₂²	semidirect
95. C₇×#518	C₂²	semidirect
96. C₇×#518	C₂²	semidirect
97. C₇×#518	C₂²	semidirect
98. C₇×#518	C₂²	semidirect
99. C₄×C₇×#41	C₂²	semidirect
100. C₄×C₇×#41	C₂²	semidirect
103. C₂×C₄×C₇×D₄	C₂²	semidirect
104. C₂×C₄×C₇×D₄	C₂²	semidirect
105. C₂×C₄×C₇×D₄	C₂²	semidirect
106. C₂×C₄×C₇×D₄	C₂²	semidirect
107. C₂×C₄×C₇×D₄	C₂²	semidirect
108. C₂×C₄×C₇×D₄	C₂²	semidirect
109. C₂×C₇×#117	C₂²	semidirect
110. C₂×C₇×#117	C₂²	semidirect
111. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
112. C₂²×C₇×C₂²⋊C₄	C₂²	semidirect
113. #62846	C₇	direct (N × H)
118. C₂×C₇×#41	C₂³	semidirect
119. C₂×C₇×#41	C₂³	semidirect
120. C₂²×C₇×Q₈	C₂³	semidirect
130. C₂²×C₇×D₄	C₂³	semidirect
136. C₂³×C₄×C₇	C₂³	semidirect
137. C₇×C₄⋊Q₈	C₂³	semidirect
138. C₇×C₄⋊Q₈	C₂³	semidirect
139. C₇×C₄⋊Q₈	C₂³	semidirect
140. C₇×C₄⋊Q₈	C₂³	semidirect
142. C₇×#127	C₂³	semidirect
146. C₇×#126	C₂³	semidirect
147. C₇×#126	C₂³	semidirect
148. C₇×#126	C₂³	semidirect
149. C₇×#126	C₂³	semidirect
150. C₇×#126	C₂³	semidirect
151. C₇×#125	C₂³	semidirect
152. C₇×#125	C₂³	semidirect
153. C₇×#125	C₂³	semidirect
154. C₇×#125	C₂³	semidirect
155. C₇×#125	C₂³	semidirect
160. C₇×#124	C₂³	semidirect
161. C₇×#124	C₂³	semidirect
162. C₇×#124	C₂³	semidirect
163. C₇×#124	C₂³	semidirect
169. C₇×#123	C₂³	semidirect
170. C₇×#123	C₂³	semidirect
171. C₇×#123	C₂³	semidirect
172. C₇×#123	C₂³	semidirect
173. C₇×#123	C₂³	semidirect
174. C₇×#123	C₂³	semidirect
175. C₇×#123	C₂³	semidirect
181. C₇×C₂²⋊Q₈	C₂³	semidirect
182. C₇×C₂²⋊Q₈	C₂³	semidirect
183. C₇×C₂²⋊Q₈	C₂³	semidirect
184. C₇×C₂²⋊Q₈	C₂³	semidirect
185. C₇×C₂²⋊Q₈	C₂³	semidirect
186. C₇×C₂²⋊Q₈	C₂³	semidirect
187. C₇×C₂²⋊Q₈	C₂³	semidirect
188. C₇×C₂²⋊Q₈	C₂³	semidirect
189. C₇×C₂²⋊Q₈	C₂³	semidirect
202. C₇×#121	C₂³	semidirect
203. C₇×#121	C₂³	semidirect
204. C₇×#121	C₂³	semidirect
205. C₇×#121	C₂³	semidirect
206. C₇×#121	C₂³	semidirect
207. C₇×#121	C₂³	semidirect
208. C₇×#121	C₂³	semidirect
214. C₇×#120	C₂³	semidirect
215. C₄×C₇×Q₈	C₂³	semidirect
216. C₄×C₇×Q₈	C₂³	semidirect
217. C₄×C₇×Q₈	C₂³	semidirect
218. C₄×C₇×Q₈	C₂³	semidirect
219. C₄×C₇×Q₈	C₂³	semidirect
220. C₄×C₇×Q₈	C₂³	semidirect
237. C₄×C₇×D₄	C₂³	semidirect
238. C₄×C₇×D₄	C₂³	semidirect
239. C₄×C₇×D₄	C₂³	semidirect
240. C₄×C₇×D₄	C₂³	semidirect
241. C₄×C₇×D₄	C₂³	semidirect
242. C₄×C₇×D₄	C₂³	semidirect
243. C₄×C₇×D₄	C₂³	semidirect
244. C₄×C₇×D₄	C₂³	semidirect
245. C₄×C₇×D₄	C₂³	semidirect
246. C₄×C₇×D₄	C₂³	semidirect
247. C₄×C₇×D₄	C₂³	semidirect
248. C₄×C₇×D₄	C₂³	semidirect
253. C₇×#117	C₂³	semidirect
254. C₇×#117	C₂³	semidirect
255. C₇×#117	C₂³	semidirect
256. C₇×#117	C₂³	semidirect
257. C₇×#117	C₂³	semidirect
258. C₇×#117	C₂³	semidirect
263. C₂×C₇×C₄⋊C₄	C₂³	semidirect
264. C₂×C₇×C₄⋊C₄	C₂³	semidirect
265. C₂×C₇×C₄⋊C₄	C₂³	semidirect
266. C₂×C₇×C₄⋊C₄	C₂³	semidirect
267. C₂×C₇×C₄⋊C₄	C₂³	semidirect
281. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
282. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
283. C₂×C₇×C₂²⋊C₄	C₂³	semidirect
287. C₂×C₄²×C₇	C₂³	semidirect
288. C₂×C₄²×C₇	C₂³	semidirect
289. #3521	C₂×C₇	semidirect
290. #3519	C₂×C₇	semidirect
291. #3514	C₂×C₇	semidirect
292. #3513	C₂×C₇	semidirect
293. #3506	C₂×C₇	semidirect
294. #3505	C₂×C₇	semidirect
295. #3501	C₂×C₇	semidirect
296. #3496	C₂×C₇	semidirect
297. #3493	C₂×C₇	semidirect
298. #3490	C₂×C₇	semidirect
299. #3484	C₂×C₇	semidirect
300. #3460	C₂×C₇	semidirect
301. #3459	C₂×C₇	semidirect
302. #3455	C₂×C₇	semidirect
303. C₂×#538	C₂×C₇	semidirect
304. C₄×H(5,𝔽₂)	C₂×C₇	semidirect
305. C₂×#518	C₂×C₇	semidirect
331. C₂×C₇×D₄	#41	semidirect
426. #559	C₂²×C₇	semidirect
427. #556	C₂²×C₇	semidirect
428. #556	C₂²×C₇	semidirect
429. #555	C₂²×C₇	semidirect
430. #555	C₂²×C₇	semidirect
431. #554	C₂²×C₇	semidirect
432. #554	C₂²×C₇	semidirect
433. #553	C₂²×C₇	semidirect
434. #553	C₂²×C₇	semidirect
435. #553	C₂²×C₇	semidirect
436. #553	C₂²×C₇	semidirect
437. #552	C₂²×C₇	semidirect
438. #552	C₂²×C₇	semidirect
439. #551	C₂²×C₇	semidirect
440. #551	C₂²×C₇	semidirect
441. #551	C₂²×C₇	semidirect
442. #550	C₂²×C₇	semidirect
443. D₄×Q₈	C₂²×C₇	semidirect
444. #548	C₂²×C₇	semidirect
445. #547	C₂²×C₇	semidirect
446. #547	C₂²×C₇	semidirect
447. #546	C₂²×C₇	semidirect
448. #546	C₂²×C₇	semidirect
449. #546	C₂²×C₇	semidirect
450. #546	C₂²×C₇	semidirect
451. #546	C₂²×C₇	semidirect
452. #546	C₂²×C₇	semidirect
453. D₄²	C₂²×C₇	semidirect
454. D₄²	C₂²×C₇	semidirect
455. D₄²	C₂²×C₇	semidirect
456. #544	C₂²×C₇	semidirect
457. #543	C₂²×C₇	semidirect
458. #542	C₂²×C₇	semidirect
459. #542	C₂²×C₇	semidirect
460. #542	C₂²×C₇	semidirect
461. #541	C₂²×C₇	semidirect
462. #540	C₂²×C₇	semidirect
463. #540	C₂²×C₇	semidirect
464. #539	C₂²×C₇	semidirect
465. #539	C₂²×C₇	semidirect
466. #539	C₂²×C₇	semidirect
467. #538	C₂²×C₇	semidirect
468. #538	C₂²×C₇	semidirect
469. #538	C₂²×C₇	semidirect
470. #538	C₂²×C₇	semidirect
471. #538	C₂²×C₇	semidirect
472. #538	C₂²×C₇	semidirect
473. #538	C₂²×C₇	semidirect
474. #538	C₂²×C₇	semidirect
475. #537	C₂²×C₇	semidirect
476. #535	C₂²×C₇	semidirect
477. #534	C₂²×C₇	semidirect
478. #534	C₂²×C₇	semidirect
479. #533	C₂²×C₇	semidirect
480. #532	C₂²×C₇	semidirect
481. #532	C₂²×C₇	semidirect
482. #529	C₂²×C₇	semidirect
483. #529	C₂²×C₇	semidirect
484. #529	C₂²×C₇	semidirect
485. #529	C₂²×C₇	semidirect
486. #529	C₂²×C₇	semidirect
487. C₂×#126	C₂²×C₇	semidirect
488. C₂×#124	C₂²×C₇	semidirect
489. #525	C₂²×C₇	semidirect
490. #525	C₂²×C₇	semidirect
491. #525	C₂²×C₇	semidirect
492. #525	C₂²×C₇	semidirect
493. C₂×#123	C₂²×C₇	semidirect
494. C₂×C₂²⋊Q₈	C₂²×C₇	semidirect
495. C₂×#121	C₂²×C₇	semidirect
496. C₂×#121	C₂²×C₇	semidirect
497. C₂×#120	C₂²×C₇	semidirect
498. #520	C₂²×C₇	semidirect
499. #520	C₂²×C₇	semidirect
501. #518	C₂²×C₇	semidirect
502. #518	C₂²×C₇	semidirect
503. #518	C₂²×C₇	semidirect
504. #518	C₂²×C₇	semidirect
505. C₄×#41	C₂²×C₇	semidirect
506. C₄×#41	C₂²×C₇	semidirect
509. C₂×C₄×D₄	C₂²×C₇	semidirect
510. C₂×C₄×D₄	C₂²×C₇	semidirect
511. C₂×C₄×D₄	C₂²×C₇	semidirect
512. C₂×C₄×D₄	C₂²×C₇	semidirect
513. C₂×C₄×D₄	C₂²×C₇	semidirect
514. C₂×C₄×D₄	C₂²×C₇	semidirect
515. C₂×#117	C₂²×C₇	semidirect
516. C₂×#117	C₂²×C₇	semidirect
517. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
518. C₂²×C₂²⋊C₄	C₂²×C₇	semidirect
594. C₂×#41	C₂³×C₇	semidirect
595. C₂×#41	C₂³×C₇	semidirect
596. C₂²×Q₈	C₂³×C₇	semidirect
606. C₂²×D₄	C₂³×C₇	semidirect
612. C₂³×C₄	C₂³×C₇	semidirect
613. C₄⋊Q₈	C₂³×C₇	semidirect
614. C₄⋊Q₈	C₂³×C₇	semidirect
615. C₄⋊Q₈	C₂³×C₇	semidirect
616. C₄⋊Q₈	C₂³×C₇	semidirect
618. #127	C₂³×C₇	semidirect
622. #126	C₂³×C₇	semidirect
623. #126	C₂³×C₇	semidirect
624. #126	C₂³×C₇	semidirect
625. #126	C₂³×C₇	semidirect
626. #126	C₂³×C₇	semidirect
627. #125	C₂³×C₇	semidirect
628. #125	C₂³×C₇	semidirect
629. #125	C₂³×C₇	semidirect
630. #125	C₂³×C₇	semidirect
631. #125	C₂³×C₇	semidirect
636. #124	C₂³×C₇	semidirect
637. #124	C₂³×C₇	semidirect
638. #124	C₂³×C₇	semidirect
639. #124	C₂³×C₇	semidirect
645. #123	C₂³×C₇	semidirect
646. #123	C₂³×C₇	semidirect
647. #123	C₂³×C₇	semidirect
648. #123	C₂³×C₇	semidirect
649. #123	C₂³×C₇	semidirect
650. #123	C₂³×C₇	semidirect
651. #123	C₂³×C₇	semidirect
657. C₂²⋊Q₈	C₂³×C₇	semidirect
658. C₂²⋊Q₈	C₂³×C₇	semidirect
659. C₂²⋊Q₈	C₂³×C₇	semidirect
660. C₂²⋊Q₈	C₂³×C₇	semidirect
661. C₂²⋊Q₈	C₂³×C₇	semidirect
662. C₂²⋊Q₈	C₂³×C₇	semidirect
663. C₂²⋊Q₈	C₂³×C₇	semidirect
664. C₂²⋊Q₈	C₂³×C₇	semidirect
665. C₂²⋊Q₈	C₂³×C₇	semidirect
678. #121	C₂³×C₇	semidirect
679. #121	C₂³×C₇	semidirect
680. #121	C₂³×C₇	semidirect
681. #121	C₂³×C₇	semidirect
682. #121	C₂³×C₇	semidirect
683. #121	C₂³×C₇	semidirect
684. #121	C₂³×C₇	semidirect
690. #120	C₂³×C₇	semidirect
691. C₄×Q₈	C₂³×C₇	semidirect
692. C₄×Q₈	C₂³×C₇	semidirect
693. C₄×Q₈	C₂³×C₇	semidirect
694. C₄×Q₈	C₂³×C₇	semidirect
695. C₄×Q₈	C₂³×C₇	semidirect
696. C₄×Q₈	C₂³×C₇	semidirect
713. C₄×D₄	C₂³×C₇	semidirect
714. C₄×D₄	C₂³×C₇	semidirect
715. C₄×D₄	C₂³×C₇	semidirect
716. C₄×D₄	C₂³×C₇	semidirect
717. C₄×D₄	C₂³×C₇	semidirect
718. C₄×D₄	C₂³×C₇	semidirect
719. C₄×D₄	C₂³×C₇	semidirect
720. C₄×D₄	C₂³×C₇	semidirect
721. C₄×D₄	C₂³×C₇	semidirect
722. C₄×D₄	C₂³×C₇	semidirect
723. C₄×D₄	C₂³×C₇	semidirect
724. C₄×D₄	C₂³×C₇	semidirect
729. #117	C₂³×C₇	semidirect
730. #117	C₂³×C₇	semidirect
731. #117	C₂³×C₇	semidirect
732. #117	C₂³×C₇	semidirect
733. #117	C₂³×C₇	semidirect
734. #117	C₂³×C₇	semidirect
739. C₂×C₄⋊C₄	C₂³×C₇	semidirect
740. C₂×C₄⋊C₄	C₂³×C₇	semidirect
741. C₂×C₄⋊C₄	C₂³×C₇	semidirect
742. C₂×C₄⋊C₄	C₂³×C₇	semidirect
743. C₂×C₄⋊C₄	C₂³×C₇	semidirect
757. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
758. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
759. C₂×C₂²⋊C₄	C₂³×C₇	semidirect
763. C₂×C₄²	C₂³×C₇	semidirect
764. C₂×C₄²	C₂³×C₇	semidirect
823. C₂×D₄	C₇×#41	semidirect
995. C₇	#62846	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₇×#3521	2
C₇×#3519	2
C₇×#3514	2
C₇×#3513	2
C₇×#3506	2
C₇×#3505	2
C₇×#3501	2
C₇×#3496	2
C₇×#3493	2
C₇×#3490	2
C₇×#3484	2
C₇×#3460	2
C₇×#3459	2
C₇×#3455	2
C₂×C₇×#538	2
C₄×C₇×H(5,𝔽₂)	2
C₂×C₇×#518	2
#62846	7

Subgroups — C7×#62846 #13240062

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₇×#62846 #13240062